Calculating profit maximizing price and quantity relationship

any firm, whether perfectly competitive or not. Profit (π) = Total Revenue - Total Cost. If q is output of the firm, then total revenue is price of the good times quantity . There is a very simple rule to find the level of output that maximizes profits at a given . is the exact formula of the relationship between total cost and quantity. (We use Π to stand for profit because we use P for something else: price.) Total revenue . [Note: For this reason, some textbooks use a slightly different formula.

To find the value of that maximizes this function, we differentiate with respect to using the product differentiation rule,: The first-order condition for optimization iswhich may be rearranged as follows: The profit-maximizing quantity,satisfies this equation.

If we knew the specific form of the functions andwe could try to solve the equation to find explicitly. The profit-maximizing price could then be calculated as. But without knowing the functions, we can still interpret the first-order condition.

We know that the optimal value of is on the demand curve, soand that is marginal cost MC. So the first-order condition can be written: The left-hand side of this equation is the slope of the demand curve.

The Economy: Leibniz: The profit-maximizing price

We showed in Leibniz 7. Thus the first-order condition tells us precisely that the profit-maximizing choice lies at a point of tangency between the demand and isoprofit curves. For Beautiful Cars, this is point E in Figure 7. The profit-maximizing choice of price and quantity for Beautiful Cars. Figure 1 The profit-maximizing choice of price and quantity for Beautiful Cars.

Thus, consumers will suffer from a monopoly because a lower quantity will be sold in the market, at a higher price, than would have been the case in a perfectly competitive market. The problem of inefficiency for monopolies often runs even deeper than these issues, and also involves incentives for efficiency over longer periods of time.

There are counterbalancing incentives here. On one side, firms may strive for new inventions and new intellectual property because they want to become monopolies and earn high profits—at least for a few years until the competition catches up. In this way, monopolies may come to exist because of competitive pressures on firms. However, once a barrier to entry is in place, a monopoly that does not need to fear competition can just produce the same old products in the same old way—while still ringing up a healthy rate of profit.

John Hicks, who won the Nobel Prize for economics inwrote in He meant that monopolies may bank their profits and slack off on trying to please their customers. The old joke was that you could have any color phone you wanted, as long as it was black.

An explosion of innovation followed. Services like call waiting, caller ID, three-way calling, voice mail though the phone company, mobile phones, and wireless connections to the Internet all became available. A wide range of payment plans was offered, as well. It was no longer true that all phones were black; instead, phones came in a wide variety of shapes and colors.

The end of the telephone monopoly brought lower prices, a greater quantity of services, and also a wave of innovation aimed at attracting and pleasing customers. The Rest is History In the opening case, the East India Company and the Confederate States were presented as a monopoly or near monopoly provider of a good. Regarding the cotton industry, we also know Great Britain remained neutral during the Civil War, taking neither side during the conflict.

Did the monopoly nature of these business have unintended and historical consequences? Might the American Revolution have been deterred, if the East India Company had sailed the tea-bearing ships back to England? Of course, it is not possible to definitively answer these questions; after all we cannot roll back the clock and try a different scenario.

We can, however, consider the monopoly nature of these businesses and the roles they played and hypothesize about what might have occurred under different circumstances.

Perhaps if there had been legal free tea trade, the colonists would have seen things differently; there was smuggled Dutch tea in the colonial market. If the colonists had been able to freely purchase Dutch tea, they would have paid lower prices and avoided the tax. What about the cotton monopoly? With one in five jobs in Great Britain depending on Southern cotton and the Confederate States nearly the sole provider of that cotton, why did Great Britain remain neutral during the Civil War?

At the beginning of the war, Britain simply drew down massive stores of cotton. These stockpiles lasted until near the end of Why did Britain not recognize the Confederacy at that point? The Emancipation Proclamation and new sources of cotton. Having outlawed slavery throughout the United Kingdom init was politically impossible for Great Britain, empty cotton warehouses or not, to recognize, diplomatically, the Confederate States.

In addition, during the two years it took to draw down the stockpiles, Britain expanded cotton imports from India, Egypt, and Brazil. Monopoly sellers often see no threats to their superior marketplace position.

In these examples did the power of the monopoly blind the decision makers to other possibilities? But, as they say, the rest is history. Key Concepts and Summary[ edit ] A monopolist is not a price taker, because when it decides what quantity to produce, it also determines the market price. For a monopolist, total revenue is relatively low at low quantities of output, because not much is being sold.

Maximizing Profit Practice- Micro 3.9

Total revenue is also relatively low at very high quantities of output, because a very high quantity will sell only at a low price. Thus, total revenue for a monopolist will start low, rise, and then decline.

The marginal revenue for a monopolist from selling additional units will decline.

solving for price, quantity, revenue, and costs – College-Cram Students

Each additional unit sold by a monopolist will push down the overall market price, and as more units are sold, this lower price applies to more and more units. If that price is above average cost, the monopolist earns positive profits.

Monopolists are not productively efficient, because they do not produce at the minimum of the average cost curve. As a result, monopolists produce less, at a higher average cost, and charge a higher price than would a combination of firms in a perfectly competitive industry.

solving for price, quantity, revenue, and costs

Monopolists also may lack incentives for innovation, because they need not fear entry. How much output should the firm supply? If price falls below AVC, the firm will not be able to earn enough revenues even to cover its variable costs. In such a case, it will suffer a smaller loss if it shuts down and produces no output.

If it shuts down, it only loses its fixed costs. Imagine a monopolist could charge a different price to every customer based on how much he or she were willing to pay. How would this affect monopoly profits? However, there would be no consumer surplus since each buyer is paying exactly what they think the product is worth. Therefore, the monopolist would be earning the maximum possible profits. Review Questions[ edit ] How is the demand curve perceived by a perfectly competitive firm different from the demand curve perceived by a monopolist?

Principles of Microeconomics/How a Profit-Maximizing Monopoly Chooses Output and Price

How does the demand curve perceived by a monopolist compare with the market demand curve? Is a monopolist a price taker? What is the usual shape of a total revenue curve for a monopolist?